The fundamental problem in holography is to record an object wavefront and then reconstruct the same physically. The basic solution of this problem has been given by D. Gabor (Nature 161 (1948) 777), and involves mixing the object wave U.sub.o (x,y) with an on-axis reference wave U.sub.r (x,y) in a recording device whose transfer function is proportional to the total intensity I(x,y): EQU I(x,y)=.vertline.U.sub.r +U.sub.o .vertline..sup.2 =U.sub.r .vertline..sup.2 +.vertline.U.sub.o .vertline..sup.2 +U.sub.r *U.sub.o +U.sub.r U.sub.o * (1)
The recording device forms the hologram of the object wave. By illuminating the hologram with an on-axis reconstruction wave U.sub.s (x,y), the object wave is reconstructed. The total wave obtained from the hologram is proportional to U(x,y): EQU U(x,y)=U.sub.s .vertline.U.sub.r .vertline..sup.2 +U.sub.s .vertline.U.sub.o .vertline..sup.2 +U.sub.r U.sub.s U.sub.o *+U.sub.r *U.sub.s U.sub.o ( 2)
or: EQU U(x,y)=U.sub.r .vertline.U.sub.r .vertline..sup.2 +U.sub.r .vertline.U.sub.o .vertline..sup.2 +U.sub.r.sup.2 U.sub.o *+.vertline.U.sub.r .vertline..sup.2 U.sub.o ( 3)
when U.sub.s (x,y)=U.sub.r x,y), according to Gabor.
The two last terms of equation (2) represent one virtual and one real image of the object, or both represent two virtual or two real images, depending upon the reference and reconstruction waves (R. W. Meier, J., Opt. Soc. Am. 56 (1966) 219). The corresponding terms in equation (3) result in one virtual image and one real image which overlap each other. The problem of overlapping images was solved by E. N. Leith and J. Upatnieks (J. Opt. Soc. Am. 52 (1962) 1123) who introduced off-axis reference and reconstruction waves: EQU U.sub.r =U.sub.s =Ae.sup.jk(.alpha.x+.beta.y+.gamma.z) ( 4)
where
a=the amplitude, PA1 k=2.pi./.lambda. with .lambda.=wavelength, and PA1 .alpha., .beta., .gamma. are the direction cosines.
This expression included in equation (2) or (3) shows that all reconstructed images are separated from each other in space.
If the hologram is recorded as a linear volume hologram, then a single image can be obtained. However, the generation of volume holograms is much more difficult than plane holograms.
The same results are obtained in digital holography when the analog holographic technique is copied. As is known, the principle of digital holography concerns sampling of the object wavefront, calculation of the corresponding hologram points and registration of these in a medium which is to form the hologram. By illuminating the hologram with the reconstruction wave the wavefront is reconstructed physically as virtual, real and higher order images. It is also possible to calculate the reconstructed wavefront in the computer and to display the result in a display unit.
Since digital holography is not limited to the use of physical waves during the production of the hologram, it has been shown possible to produce holograms that yield reconstruction of only one image. In the kineform method (L. B. Lesem, P. M. Hirsch, J. A. Jordan, Jr., IBM J. res. Develop. 13 (1969) 150) where the reconstructed wave emanating from the hologram is described as EQU U(x,y)=A(x,y,z)e.sup.j.phi.(x,y,z) ( 5)
it is assumed that the information comes mainly from the phase .phi.(x,y,z), and the amplitude A(x,y,z) is taken to be constant. The calculated phase is quantized into a certain number of grey levels which are then produced as hologram points on a photographic film. However, the method represents a rather tedious process. Another solution described by D. C. Chu, J. R. Fienup and J. W. Goodman (Appl. Opt. 12 (1973) 1386) concerns the use of two photographic emulsions for separate control of amplitude and phase. However, it is difficult to align the two emulsions. In most other methods both the real and virtual images are reproduced, as well as higher order images whenever the transfer function of the hologram is nonlinear. There has consequently existed a need for a simple holographic method that results in a more satisfactory reconstruction of the object wave.
It is also desirable to be able to reconstruct only the image of one object at a time when a number of wavefronts of different objects are recorded in the same hologram and to be able to scan from one image to another in a simple fashion.